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Talk:Leibniz's rule (derivatives and integrals)

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Can someone tell me, please, the source from which this proof has been copied? I have some books of analysis and their proofs of this theorem are not so simple. It would be excellent to be sure that we really have an easier proof. Castilla.


I think it would be necesary to proof that uniform continuity allows you to change the limit from the left side of the integral to the right side.

I do not see how uniform continuity allows you to state that.

spelling

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shouldn't it read Leibniz' rule? MFH: Talk 22:39, 10 May 2005 (UTC)[reply]

Why? Even if his name was Leibnis, there is one convention that dictates to write "Leibnis's", the other being to write "Leibnis'" -- but his name is not spelt Leibnis, it's spelt Leibniz. Dysprosia 03:06, 11 May 2005 (UTC)[reply]

Sorry, but I learned it like this: the Genitive s is omitted after the apostrophe if the word ends in an "-s" sound (the reason for the dropped "s" being of course an issue of pronounciation and not of writing). And IMHO, z and tz etc. end in an "-s" sound. Now, you may be right, but I'm curious about how you pronounce this... MFH: Talk 20:11, 11 May 2005 (UTC)[reply]

The /z/ and /tz/ sounds do not end in the softer /s/ sound, I believe. Dysprosia 21:47, 11 May 2005 (UTC)[reply]

See http://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign too. These all should be one.

The alternate form isn't one

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The given alternate form:

is merely the fundamental theorem of calculus (FTC) augmented by the chain rule.

Chose any between and . Then

FTC gives us

and

So

by the chain rule.